Class-12 Ch-2 (Electric Potential and Capacitance)

📘 Chapter 2: Electric Potential and Capacitance – Class 12 Physics Notes

1. Electric Potential (V)

• Definition: Work done per unit charge in bringing a test charge from infinity to a point.
  Formula: V = W/q

• Unit: Volt (V)

• It is a scalar quantity.

2. Electric Potential Due to a Point Charge
Formula: V = (1 / 4πε₀) × (q / r)
Where:

• q = charge

• r = distance from charge

• ε₀ = permittivity of free space

3. Potential Difference (V_AB)

• Work done to move a unit positive charge from point A to B.
  Formula: V_AB = V_A – V_B = – ∫ E ⋅ dr

4. Equipotential Surfaces

• Surface with constant potential everywhere

• No work is done in moving a charge along it

• Always perpendicular to electric field lines

5. Relation Between Electric Field (E) and Potential (V)
Formula: E = -dV/dr

6. Capacitance (C)

• Ability of a system to store charge per unit potential
  Formula: C = q / V

• Unit: Farad (F)

• Scalar quantity

7. Capacitor

• A device to store electrical energy

• Common types:

  • Parallel Plate Capacitor

  • Spherical Capacitor

  • Cylindrical Capacitor

8. Capacitance of a Parallel Plate Capacitor
Without dielectric: C = ε₀ × (A / d)
With dielectric: C = Kε₀ × (A / d)
Where:

• A = area of plates

• d = distance between plates

• K = dielectric constant

9. Combination of Capacitors
(i) Series Combination:
1 / C_eq = 1 / C₁ + 1 / C₂ + 1 / C₃ + …

(ii) Parallel Combination:
C_eq = C₁ + C₂ + C₃ + …

10. Energy Stored in a Capacitor
Formula: U = (1/2) × C × V²

🧠 Key Points to Remember

• Electric potential is path-independent.

• On the surface of a charged conductor, potential is constant.

• Dielectrics increase the capacitance of a capacitor.

• Equipotential surface ⇒ no work done in movement along it.